Impact of Space-Energy Correlation on Variable Range Hopping in a Transistor

Hopping conduction in transistors, i.e., under a transverse electric field, is addressed using percolation theory with a space-energy correlation in the density of states of the impurity band. The computation of the percolation threshold over an extended range of correlation parameters enables us to derive a formula, which, while giving the classical results in the low field limit, describes the emergence of a specific variable range hopping in the high field case. An application of this formula to experimentally extract the localization radius is also proposed.

Figure 1

Computed DOS. A clear Coulomb gap is observed in (a) while it is barely perceivable in (d).

Figure 2

Computation results for a wide range of $1/C$. (a) $N_c/A^2$ against $1/C$, extracted for constant $W$’s. Dots are computation results and lines are values from Eq. (3). The position of the planes where $W$ is constant is shown in (b). (b) $N_c/A^2$ against $W/C$ and $1/C$. Crosses are computation results and dots are values from Eq. (3). The planes of constant $W$ for (a) are exhibited. Inset in (a): Model DOS $g(\epsilon ,z)$. The current flows perpendicularly to the page.

Figure 3

Computation results for $N_c/A^2$ against $C$ and $W$, for the high-slope limit. (a) Computation results and (b) values extracted from Eq. (3). An offset in $N_c/A^2$ is visible.